English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A complex contact structure $\gamma$ is defined by a system of holomorphic local $1$-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle ${\rm Ker}\, \gamma$ of the tangent bundle and a line bundle $L$. In this paper, we prove that the sheaf of holomorphic $k$-vectors on a complex contact manifold splits into the sum of $\mathcal{O}(\bigwedge^{k}{\rm Ker}\, \gamma)$ and $\mathcal{O}(L\otimes \bigwedge^{k-1} {\rm Ker}\, \gamma)$ as sheaves of {\it $\mathbb{C}$-module}. The theorem induces the short exact sequence of cohomology of holomorphic $k$-vectors, and we obtain vanishing theorems for the cohomology of $\mathcal{O}(\bigwedge^{k} \ker \gamma)$.

Splitting theorem for sheaves of holomorphic k-vectors on complex contact manifolds